Kayn: What am I doing wrong?

I&#039;ve got Kayn as soon as it was released. For the time passed I have at least a match per day as Kayn.
And I still can&#039;t understand... where his damage is??? How to really influence game with this champ?
Where&#039;s his power spike? What is it I am building wrong? Could you advice me on this please?
I tried building Black Cleaver {{item:3071}} .
I tried Trinity {{item:3078}} to have 20% CDR, movement and Sheen passive on hit.
I tried going tanky this way {{item:3025}} {{item:3742}}
I tried building {{item:3812}} for AD and additional LifeSteal.
I even tried going {{item:3074}}
The central problem is... I can&#039;t deal enough damage with Abilities even with 40% CDR and enough AD stacked. Going full combo: Q -&gt; aa -&gt; W -&gt; aa -&gt; E-&gt; aa -&gt; Q -&gt; aa -&gt; R --- doesn&#039;t really kill *anyone*. not even the squishiest champs. Addition of Chilling smite doesn&#039;t help much. And going R early doesn't help: they just run to their allies or under turret.
Does anyone have any personal experience of success to share? How to build? What to rely upon? Should I go auto attacks, like Tryndamere? Or should I build full tank and let others do main damage? Or change combo order, maybe? Or full lethality Rhaast?
How to carry with Kayn as Red?
{{champion:141}}

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